(25) Fourier Analysis

Waveforms that are neither even nor odd in have both

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Unformatted text preview: arise quite naturally in the theory of standing waves, because the normal modes of oscillation of any uniform continuous system possessing linear equations of motion (e.g., a uniform string, an elastic rod, an ideal gas) take the form of spatial cosine and sine waves whose wavelengths are rational fractions of one another. Thus, the instantaneous spatial waveform of such a system can always be represented as a linear superposition of cosine and sine waves: that is, a Fourier series in space, rather than in time. In fact, the process of determining the amplitudes and phases of the normal modes of oscillation from the initial conditions is essentially equivalent to Fourier analyzing the initial conditions in space. (See Sections 5.3 and 6.2.)...
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This note was uploaded on 08/25/2013 for the course PHY 315 taught by Professor Staff during the Fall '08 term at University of Texas.

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